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Correlation measurements of particle interaction at STAR

Correlation measurements of particle interaction at STAR. R. Lednický @ JINR Dubna & IP ASCR Prague. History QS correlations  femtoscopy with identical particles FSI correlations  femtoscopy with nonidentical particles Correlation study of strong interaction Summary.

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Correlation measurements of particle interaction at STAR

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  1. Correlation measurements of particle interaction at STAR R. Lednický@ JINR Dubna & IP ASCR Prague • History • QS correlations femtoscopy with identical particles • FSI correlations femtoscopy with nonidentical particles • Correlation study of strong interaction • Summary HSQCD, Gatchina, June 27-July 1, 2016

  2. History of Correlation femtoscopy measurement of space-time characteristics R, c ~ fm of particle production using particle correlations Fermi’34, GGLP’60, Dubna (GKPLL..’71-) … -decay: Coulomb FSI between e± and Nucleusin β-decay modifies the relative momentum (k) distribution → Fermi (correlation) function F(k,Z,R)=|-k(r)|2 is sensitive to Nucleusradius R if charge Z » 1 -k(r) = electron – Nucleus WF (t=0)

  3. F(k,Z,R) ) = |-k(r)|2 ~ (kR)-(Z/137)2 25 20 15 10 5 MeV k c 2 4 6 8 Fermi function in β-decay = |-k(r)|2 ~ (kR)-(Z/137)2 Fermi f-n Z=83 (Bi) β- 2 fm 4 R=8 β+

  4. Modern correlation femtoscopy formulated by Kopylov & Podgoretsky KP’71-75: settled basics of correlation femtoscopy in > 20 papers (for non-interacting identical particles)‏ • proposed CF= Ncorr /Nuncorr& mixing techniques to construct Nuncorr & two-body approximation to calculate theor. CF •showed that sufficientlysmooth momentum spectrum allows one to neglect space-time coherence at small q* smoothness approximation: |∫d4x1d4x2p1p2(x1,x2)...|2 →∫d4x1d4x2p1p2(x1,x2)|2... •clarified role of space-time production characteristics: shape & time source picture from various q-projections

  5. QS symmetrization of production amplitudemomentum correlations of identical particles are sensitive to space-time structure of the source KP’71-75 total pair spin CF=1+(-1)Scos qx exp(-ip1x1) p1 2 xA ,nns,s xB 1/R0 1 p2 2R0 nnt,t PRF q =p1- p2 → {0,2k*} x = xA - xB → {t*,r*} 0 |q| CF →  |S(sym)-k*(r*)|2  =  | [ e-ik*r* +(-1)S eik*r*]/√2 |2  ! CF of noninteracting identical particles is independent of t* in PRF

  6. KP model of single-particle emitters Probability amplitude to observe aparticle with 4-coordinatex from emitter A at xA can depend on x−xAonly and so can be written as: Transfering to 4-momentum representation:  and probabilityamplitudetoobserve two spin-0 bosons: Corresponding momentumcorrelation function: x=xA–xB if uA(p1)  uA(p2): “smoothness assumption”

  7. Assumptions to derive KP formula CF - 1  cos qx - two-particle approximation (small freeze-out PS density f) ~ OK, <f>  1 ? lowpt - smoothness approximation: Remitter  Rsource |p|  |q|peak ~ OK in HIC, Rsource20.1 fm2  pt2-slope of direct particles - neglect of FSI OK for photons, ~ OK for pions up to Coulomb repulsion - incoherent or independent emission 2 and 3 CF data approx. consistent with KP formulae: CF3(123) = 1+|F(12)|2+|F(23)|2+|F(31)|2+2Re[F(12)F(23)F(31)] CF2(12) = 1+|F(12)|2 , F(q)| = eiqx

  8. FSI: plane waves → BS-amplitude  Inserting KP amplitude T0(p1,p2;) =uA(p1)uB(p2)exp(-ip1xA-ip2xB) in Tand taking the amplitudes uA() and uB(P-) out of the integral at   p1and P-  p2 (again “smoothness assumption”)  Product of plane waves  BS-amplitude  : T(p1,p2;) =uA(p1)uB(p2)p1p2(xA, xB)

  9. RL, Lyuboshitz SJNP 35 (82) 770; RL nucl-th/0501065 Effect of nonequal times in pair cms → BS ampl. WF Applicability condition of equal-time approximation: |t*| m1,2r*2 |k*t*| m1,2r* r0=2 fm 0=2 fm/c r0=2 fm v=0.1  OK for heavy particles & small k* OK within 5% even for pions if 0 ~r0 or lower

  10. “Fermi-like” CF formula CF =  |-k*(r*)|2  Koonin’77: nonrelativistic & unpolarized protons RL, Lyuboshitz’81: generalization to relativistic & polarized & nonidentical particles & estimated the effect of nonequal times Assumptions: • same as for KP formula in case of pure QS & - equal time approximation in PRF RL, Lyuboshitz’81  eq. time conditions: |t*| m1,2r*2 |k*t*| m1,2r* OK(usually, to several % even for pions) fig. - tFSI = dd/dE >tprod tFSI (s-wave) = µf0/k*  |k*|= ½|q*| hundreds MeV/c • typical momentum RL, Lyuboshitz ..’98 transfer in production & account for coupled channels within the same isomultiplet only: + 00, -p  0n, K+K K0K0, ...

  11. |-k(r)|2 Similar to Coulomb distortion of -decay Fermi’34: Final State Interaction Migdal, Watson, Sakharov, … Koonin, GKW, LL, ... fcAc(G0+iF0) s-wave strong FSI FSI } nn e-ikr  -k(r)  [ e-ikr +f(k)eikr/r ] CF pp Coulomb |1+f/r|2 kr+kr F=1+ _______ + … eicAc ka } } Bohr radius Coulomb only Point-like Coulomb factor k=|q|/2  FSI is sensitive to source size r and scattering amplitude f It complicates CF analysis but makes possible  Femtoscopy with nonidentical particlesK,p, .. & Coalescence deuterons, .. Study “exotic” scattering,K, KK,, p,, .. • Study relative space-time asymmetriesdelays, flow

  12. Using spherical wave in the outer region (r>) & inner region (r<) correction  analytical dependence on s-wave scatt. amplitudes f0and source radius r0 LL’81 • FSI contribution to the CF of nonidentical particles, assuming Gaussian separation distribution W(r)=exp(-r2/4r02)/(2 r0)3 at kr0 << 1: CFFSI = ½|f0/r0|2[1-d0/(2r0)]+2f0/(r0) f0 & d0are the s-wave scatt. length and eff. radius determining the scattering amplitude in the effective range approximation: f0(k) = sin0exp(i0)/k  (1/f0+½d0k2 - ik)-1

  13. f0 and d0 : characterizing the nuclear force Repulsive bound state a>0 (f0<0) u(r) = eiδrψ(r) f0 = -a d0 ≈ r0 at k → 0 r > r0 u(r) ~ ( r – a) Resonance: f0 > 0 d0 < 0 V(r) V(r) u(r) u(r) V0 V0 V(r) V(r) u(r) u(r) V0 V0 No bound state a<0 (f0>0)

  14. f0 and d0 : How to measure them in scattering experiments(not always possible with reasonable statistics) Coulomb Nuclear Crossterm “Nuclear physics in a nutshell”, Carlos A. Bertulani. Princeton U Press (2007). f0 and d0 can be extracted by studying the phase shift vs. energy.

  15. Correlation analysis:a possibility to measure f0 & d0 for any abundantly produced particle pairs Correlation Function (CF): In practice, Purity correction (misidentification + ? weak decays) :

  16. Correlation femtoscopy with nonid. particles pCFs at AGS & SPS & STAR Goal: No Coulomb suppression as in pp CF & Wang-Pratt’99 Stronger sensitivity to r0 singlet triplet Scattering lengths, fm: 2.31 1.78 Fit using RL-Lyuboshitz’82 with Effective radii, fm: 3.04 3.22  consistent with estimated impurity r0~ 3-4 fm consistent with the radius from pp CF & mt scaling STAR AGS SPS =0.50.2 r0=4.50.7 fm r0=3.10.30.2 fm ‹Ref0›  0.5 fm ‹Imf0› ≈ 1 fm

  17. Pair purity problem for p CF @ STAR • PairPurity ~ 15% Assuming no correlation for misidentified particles and particles from weak decays   Fit using RL-Lyuboshitz’82(for np) • but, there can be residual correlations for particles from weak decays requiring knowledge of , p, , , p, ,  correlations

  18. +&  & p& pps-wave scattering parameters from NA49 and STAR Correlation study of strong interaction Fits using RL-Lyuboshitz’82 p: STAR data accounting for residual correlations - Kisiel et al, PRC 89(2014) : assuming a universal Imf0 - Shapoval et al, PRC 92 (2015): Gauss. parametr. of res. CF Ref0  0.5 fm, Imf0  1 fm, r0  3 fm : NA49:|f0()|  f0(NN) ~ 20 fm STAR, PRL 114 (2015): f0()  -1 fm, d0()  8 fm - +: NA49 vs RQMD with SI scale:f0siscaf0(=0.232fm) sisca = 0.60.1 compare with ~0.8 from SPT & BNL data E765 K  e Here a (2 s.d.) suppression can be due to eq. time approx. pp : STAR, Nature (2015): f0and d0 coincide with PDG table pp-values

  19. Correlation study of particle interaction CF=Norm[Purity RQMD(r* Scaler*)+1-Purity] +scattering length f0 from NA49 CF + Fit CF(+) by RQMD with SI scale: f0siscaf0input f0input = 0.232 fm - sisca = 0.60.1 to be 0.8 from SPT & BNL E765 K  e

  20. scattering parameters f0 & d0 from STAR correlation data Correlation study of strong interaction Fit using RL-Lyuboshitz (81): CF=1+[CFFSI+SS(-1)Sexp(-r02Q2)] + ares exp(-rres2Q2) 0= ¼(1-P2) 1= ¼(3+P2) P=Polar.=0 CFFSI = 20[½|f0(k)/r0|2(1-d00/(2r0)) +2Re(f0(k)/(r0))F1(r0Q) - Im(f0(k)/r0)F2(r0Q)] fS(k)=(1/f0S+½d0Sk2 - ik)-1 k=Q/2 F1(z)=0z dx exp(x2-z2)/z F2(z)=[1-exp(-z2)]/z -  0.18,r0 3 fm,ares -0.04, rres 0.4 fm f0 -1 fm, d0 8 fm  s-wave resonance: excluded Bound state: possible

  21. Correlation study of strong pp & pp interactionat STAR - -

  22. STAR : Uniform and Large Acceptance STAR detector complex EEMC Magnet MTD BEMC TPC TOF BBC Large acceptance TPC: Full azimuthal coverage, (|η|<1.0) HFT HLT

  23. Particle Identification PID by Time Projection Chamber (TPC) and Time of Flight detector (TOF). Purity for anti-protons is over 99%.

  24. Residual pp correlation Λ π- Λ Λ p π- p p π- p p p The observed (anti)protons can come from weak decays of already correlated primary particles, hence introducing residual correlations which contaminate the CF (generally cannot be treated as a constant impurity).

  25. Residual correlation Taking dominant contributions due to residual correlation, the measured correlation function can be expressed as : where proton-proton proton-proton • Cpp(k*) and CpΛ(k*pΛ) are calculated by the Lednicky and Lyuboshitz model. • CΛΛ(k*ΛΛ) is from STAR publication (PRL 114 22301 (2015)). • Regard RpΛ and RΛΛ are equal to Rpp. • T is the corresponding tranform matirces, generated by THERMINATOR2, to transform k*pΛ to k*pp, as well as k*ΛΛ to k*pp.

  26. Residual from Λ-Λ correlation STAR Collaboration (PRL 114 22301 (2015)). • CΛΛ(k*ΛΛ) CF is taken from experimental input

  27. Transformation Matrix THERMINATOR2

  28. Connecting f0 & d0 to CF

  29. Connecting f0 & d0 to CF

  30. Correlation functions • For proton-proton CF R = 2.75 ±0.01 fm; χ2/NDF = 1.66. • For antiproton-antiproton CF R = 2.80 ±0.02 fm; f0 = 7.41 ± 0.19 fm; d0 = 2.14 ± 0.27 fm; χ2/NDF = 1.61. 1σ contour STAR Preliminary Nature 527 345 (2015)

  31. Main systematics The decomposition of systematics of this analysis: Final systematics is given by (max-min)/√12 • Other systematics that are not considered in this analysis : • Non-Coulomb electromagnetic contribution due to magnetic interactions • Vacuum polarization • Finite proton size • These effects change the f0 and d0 at the level of a few percent in total. L. Mathelitsch and B. J. VerWest, Phys. Rev. C 29, 739-745 (1984). L. HellerRev. of Mod. Phys. 39, 584-590 (1967). J. R. Bergervoet, P.C. van CampenW.A. van der Sanden, and J.J. de Swart, Phys. Rev. C 38, 15-50 (1988)

  32. f0 and d0 Nature 527 345 (2015)

  33. “This paper announces an important discovery! … offers important original contribution to the forces in antimatter!” – Nature Referee A “… significance of the results can be considered high since this is really the first and only result available on the interaction between the antiprotons ever.”– Nature Referee B “… are of fundamental interest for the whole nuclear physics community and possible even beyond for atomic physics applications or condensed matter physicists. … I think that this paper is most likely one of the five most significant papers published in the discipline this year” – Nature Referee C

  34. Summary • Assumptions behind femtoscopy theory in HIC OK at k  0 (in particular, correlation measurement recovers table values of pp scattering parameters). • Wealth of data on correlations of various particles (,K0,p,,) is available & gives unique space-time info on production characteristics thanks to the effects of QS and FSI. • Info on two-particle s-wave strong interaction of abundantly produced particles:  &  & p & pp scattering amplitudes from HIC at SPS and RHIC (on a way to solving the problem of residual correlations). A good perspective: high statistics RHIC & LHC data.

  35. Spare Slides

  36. Phase space density from CFs and spectra Bertsch’94 Lisa ..’05 <f> rises up to SPS May be high phase space density at low pt ?  ? Pion condensate or laser ? Multiboson effects on CFs spectra & multiplicities

  37. Gyulassy, Kaufmann, Wilson 1979 FSI Plane wave  Bethe-Salpeter amplitude exp(-ip1x1-ip2x2)  p1p2(x1,x2 ‏) In pair CMS, only relative quantities are relevant: q={0,2k}, x={t,r} exp(ikr)  q(t,r‏) at t = 0, the reduced B-S ampl. coincides with the usual WF: q(t=0,r‏) =[-k(r‏)]* Note: in beta-decay A  A’ + e +  t(A’)-t(e) = 0 in A rest frame  t in A’e-pair rest frame Lednicky, Lyuboshitz 1981 - Eq. time approximation t=0 is valid on condition |t|  m1,2r2 Usually OK to several % even for pions - Smoothness approx. applied also to non-id. particles

  38. Note • Formally (FSI) correlations in beta decay and multiparticle production are determined by the same (Fermi) function |-k(x)|2 • But it appears for different reasons in beta decay: a weak r-dependence of -k(r) within the nucleus volume + point like + equal time emission and in multiparticle production in usual events of HIC: a small space-time extent of the emitters compared to their separation + sufficiently small phase space density + a small effect of nonequal emission times in usual conditions

  39. Lyuboshitz-Podgoretsky’79: KsKs from KK also show FSI effect on CF of neutral kaons Goal: no Coulomb. But R (λ) may go up to 40 (100)% if neglecting FSI in BE enhancement KK (~50% KsKs) f0(980) & a0(980) RL-Lyuboshitz’81 STAR data on CF(KsKs) ALICE data on CF(KsKs) arXiv:1206.2056 arXiv.org:1506.07884 l = 1.09  0.22 r0 = 4.66 0.46 fm 5.86  0.67 fm t

  40. Even stronger effect of KK-bar FSI on KsKs correlations in pp-collisions at LHC ALICE: PLB 717 (2012) 151 e.g. for kt < 0.85 GeV/c, Nch=1-11 the neglect of FSI increases  by ~100% and Rinv by ~40%  = 0.64  0.07  1.36  0.15 > 1 ! Rinv= 0.96  0.04  1.35  0.07 fm

  41. Long tails in RQMD: r* = 21 fm for r* < 50 fm NA49 central Pb+Pb 158 AGeV vs RQMD: FSI theory OK 29 fm for r* < 500 fm Fit CF=Norm[Purity RQMD(r* Scaler*)+1-Purity] RQMD overestimatesr* by 10-20% at SPS cf ~ OK at AGS worse at RHIC Scale=0.76 Scale=0.92 Scale=0.83 p

  42. Residual charge R. Lednicky, Phys. Part. Nucl. 40, 307 (2009) B. Erazmus et al, Nucl. Phys A 583 395 (1995) The influence of the Coulomb field of the comoving charge is included in the calculation of CF.

  43. Residual from p-Λ correlation • Calculation based Lednicky and Lyuboshitz model (Sov. J. Nucl. Phys. 35 770 (1982)), with parameter-inputs from Wang & Scott (PRL 83 3138 (1999)) • Variations in the result due to the uncertainty in the input parameters have been taken into account as systematic error. Aihong Tang BNL Seminar 2015

  44. pp & pp ALICE correlation data Correlation study of strong interaction

  45. - - Summary from pp & pp • The first direct measurement of interaction between two antiprotons is performed by STAR. The force between two antiprotons is found to be attractive, and is as as strong as that between protons. Corresponding scattering length and effective range are found to agree with that for the force between protons. • Besides examining CPT from a new aspect, this measurement provides a fundamental ingredient for understanding the structure of more complex anti-nuclei and their properties.

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